Question

A metal loop is being pushed at a constant velocity into a uniform magnetic field, as shown in the figure, but is only partway into the field.

As a result of this motion:

a) End a of the resistor R is at a higher potential than end b.

b) End b of the resistor R is at a higher potential than end a.

c) Ends a and b are at the same potential.

Answer 1

Concepts and reason

The concepts used to solve this problem are Faraday’s law of induction and Lenz’s law.

Use Faraday’s law and Lenz’s law to find the incorrect options.

Use Lenz’s law to find the correct option.

Fundamentals

“Faraday’s law of induction states that whenever there is a change in the magnetic flux enclosed by a circuit, an emf will induce in the circuit, and this emf is proportional to the negative of the rate of change of the magnetic flux.”

“Lenz’s law states that the magnetic field of induced current due to change in magnetic flux will act in the direction opposite to the original magnetic flux.”

The incorrect options are as follows:

• (b)End b of the resistor $R$ is at a higher potential than end b.

• (c)Ends a and b are at the same potential.

Faraday’s law states that the changing magnetic field induces an electric field. If there is a conductor in a closed circuit in the space of changing magnetic fields, there will an induced emf across the conductor.

Thus, there will a current across the conductor. Lenz’s law explains about the direction of the induced currents.

The induced current is in clockwise direction. Hence, the above options are incorrect.

If the loop is moving toward the field, then the direction of the magnetic field increases out of the plane.

From Lenz’s law, to oppose the magnetic field, a clockwise current will be induced in the loop.

Therefore, while entering the field, current flows in the loop.

The clockwise currents will flow through the rectangular loop. The current flows from higher potential to lower potential. Hence, the correct option is as follows:

• (a)End a of the resistor $R$ is at a higher potential than the end b.

Ans:

The end a of the resistor $R$ is at a higher potential than the end b.